Transcript Development of a Chromaticity measurement application

Development of a Chromaticity
measurement application using
Head-Tail phase shift technique.
Overview
• Discussion of measurement needs in the
Tevatron
• Introduction to Theory of Head-Tail Phase
Shift
• Results from initial tests in the Tevatron
• Coupling and Bunch Amplitude profiles
• Limitations of current set-up
• Conclusion
Measurement needs in the
Tevatron
• Moving from uncoalesced to coalesced
protons during machine tune-up
• Measurement during Acceleration ramp.
- Chromaticity, Tune, and Coupling.
• Current RF chromaticity system draw-backs
- Requires uncoalesced protons
- Requires three acceleration ramps.
Longitudinal Beam Dynamics
DP/P
ws
H
T
t
Longitudinal ‘phase-space’ Graph
Chromaticity Measurement Using Head-Tail Phase Shift
In the presence of non-zero chromaticity the betatron equation of motion
becomes:



Y   cos2n  wot (cos(2nqs )  1)



Thus from phase difference between two locations in a bunch the
chromaticity can be calculated:
D
  
wo Dt (cos(2nqs )  1)
Extracting Transverse position
Using the vertical and horizontal strip-line detectors installed in the
Tevatron at the F0 location we extract a profile of the transverse
behavior of the beam over a single longitudinal bunch.
The Raw Signal is Processed to remove the Reflected Signal
Sum Signal (A-plate + B-plate)
0.4
0.2
Sj
RSj
0
0.2
0.4
0
10
20
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90
j
Reconstructed Signal
0.1
Dj
RD j
0
0.1
0
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20
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j
Difference Signal (A-plate – B-plate)
70
80
90
Reflected Signal
Turn b y Turn Su m(A +B) P rofi le from St ri p-li ne mo n it or
S
From the Sum and Difference (A-plate  B-plate) Signals the Transverse
position can be calculated using:
X n, t   27  G 
Difference An, t  Bn, t 
Sum An, t  Bn, t 
Here G is the ratio of the A-B gain over the A+B gain.Once the
Transverse Position as a function of longitudinal bunch position is
known (t) we can use this to analyze the phase shift between the Head
and the Tail to Calculate Chromaticity.
Vertical and Horizontal turn by turn position after horizontal 1.6 mm kick
4
2
Centeri
0
2
0
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i
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2.5
Centeryi
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1.5
1
0
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i
Vertical and Horizontal turn by turn position after vertical 1.75 mm kick
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2
Am
Centeri
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0
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i
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Centeryi
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i
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Difference in Head Tail Phase Evolution
Q'=7.49
120
Difference in Phase (Degrees)
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0
0
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400
-20
-40
Turn Number
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Chromaticity Calculation
Q'=7.49
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10
Q'
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6
4
Take Average Across 40 Turns around 1/2 Synchrotron Period
Q' = 7.49
2
0
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Turn Number
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310
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Horizontal Measured Chrom.
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10
8
RF
Head Tail
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4
2
0
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Horizontal Chrom. Set point
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10
Vertical Measured Chrom.
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8
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6
RF
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Head Tail
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3
2
1
0
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27
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Vertical Chrom. Set point
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35
Other measurements
• Coupling
X max | 1  2 |
| DQmin |
Ymax
• Bunch Amplitude
A
j  mm

1
4 sin  

 X
2
j 1  mm
X
j1  mm
 2 X

j  mm
2

 tan    X
2
j 1  mm
X

j1  mm
2
Color Contour Plot of Bunch Amplitude after 1.6 mm
Horizontal kick after first 2.5 sec of ramp.
A
Ay
Instability Studies Performed Last Spring: (Jim Crisp, Peter Ivanov)
A
Cv=-0.93 Ch=5.1
A
Cv= -2.1 Ch = 6.2
A
Cv = -5.1 Ch = 6.2
A
Cv =-6.43 Ch =6.3
Results from most recent tests during ramp:
Tunes up the ramp
0.59
0.588
0.586
0.584
0.582
0.58
Qx
0.578
Qy
0.576
0.574
0.572
0.57
0.568
0
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GeV
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Coupling up the ramp
0.007
0.006
0.005
0.004
0.003
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0.001
0
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GeV
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Chromaticity up the ramp
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10
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AvgCx
AvgCy
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0
0
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GeV
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Timing of E17 vertical kicker
E17 kicker delay vs. Voltage
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micro secs of delay
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0
0
1
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kV
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Screen Shots of Software
Limitations of current set-up
• The major drawback of this system of
measurement is its destructiveness. For
measurement during tune up current system
is ok. For a store we need more work.
• In addition both the kickers and scope have
limitations which restrict operations.
F17 and E17 kickers
• The Horizontal kicker requires a ramp up time of
2.5 secs. (~30 possible horiz. Meas.)
• The E17 kicker produces a half sinusoid current
pulse with a base width of 10 micro secs. The F17
kicker produces a square current pulse with a
width of 1.8 micro secs.
• Thus the E17 kicker is too slow hit only one bunch
during 36x36 store. But the F17 kicker could
accomplish this if fired at the right time in the
abort gap.
Scope
• With all four channels Scope can store only
12048 turns which means the max number
of measurements possible is 23 (everyother-turn).
• The scope resolution is limited by the bit
size and closed-orbit offset which set our
minimum resolution to .1 mm.
Moving towards less destructive
measurements
• By removing the closed-orbit current offset we
should be able to reduce this resolution down to
the signal noise floor from the beam and cables.
Thus we could increase effective scope resolution
and possibly reduce the required kick amplitude.
• Excite beam adiabatically (ac dipole technique)
• Run the damper kickers resonantly. This method
of chirp excitation has been tested successfully at
HERA . Can be gated to hit only one bunch.
Conclusion
• This system is nearing completion
– Last major issue: E17 kicker timing
– Rigrous comparison with RF technique on ramp.
• Now time for beam physics studies:
– Study chromaticity and coupling changes during ramp.
– Study of Bunch amplitude using color contour plots
• Possible future improvements
– Minimally destructive measurements
– Measure beam-beam effects on chromaticity and
coupling.
– Measure Pbars?